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On the Parameterized Complexity of Biclique Cover and Partition *

unpublished

In

fatcat:bkhuvovfhvhulagr4ifedzp76u
*the*BicliquePartition problem, we have*the*additional constraint that each edge should appear in exactly*one**of**the*k*bicliques*. ... We build*on*this kernel*and*improve*the*running time for BicliquePartition to O * (2 2k 2 +k log k+k) by exploiting a linear algebraic view*on*this problem. ...*On**the**Parameterized**Complexity**of**Biclique**Cover**and**Partition*E(G 2 ) can be*covered*by 2 log 2 m*bicliques*in polynomial time by Lemma 12. ...##
###
Covering graphs with few complete bipartite subgraphs

2009
*
Theoretical Computer Science
*

Given a graph

doi:10.1016/j.tcs.2008.12.059
fatcat:ppshskddmbakfj5r2e2pheenb4
*and*an integer k,*the**biclique**cover*problem asks whether*the*edge-set*of**the*graph can be*covered*with at most k*bicliques*;*the**biclique**partition*problem is defined similarly with*the*additional ... In this paper, we investigate them in*the*framework*of**parameterized**complexity*: do*the*problems become easier if k is assumed to be small? ...*The*second author's research was supported by International Science Programme (ISP)*of*Sweden, under*the*project ''*The*Eastern African Universities Mathematics Programme (EAUMP).'' ...##
###
Covering Graphs with Few Complete Bipartite Subgraphs
[chapter]

2007
*
Lecture Notes in Computer Science
*

In this paper we investigate them in

doi:10.1007/978-3-540-77050-3_28
fatcat:3veh3svmendplpbl6ogtow6hhy
*the*framework*of**parameterized**complexity*: do*the*problems become easier if k is assumed to be small? ... We observe that*the**Biclique*Vertex-*Cover**and**Biclique*Vertex-*Partition*problem are equivalent, since we can always make*the**bicliques**of*a*biclique*vertex-*cover*disjoint without increasing*the*size*of*... Acknowledgment*The*authors thank Mike Fellows for helpful discussions. ...##
###
Mod/Resc Parsimony Inference
[chapter]

2010
*
Lecture Notes in Computer Science
*

We show that this is formally equivalent to

doi:10.1007/978-3-642-13509-5_19
fatcat:mt3u524dffgrlhy7cnn6xor7ye
*the*Bipartite*Biclique*Edge*Cover*problem*and*derive some*complexity*results for our problem using this equivalence. ... defined operation*on*these matrices gives back*the*input. ... [8] studied*the*Bipartite*Biclique*Edge*Cover*problem in*the*context*of**parameterized**complexity*. ...##
###
Exact Algorithms for Biclique Coloring

2022
*
Matemática contemporânea
*

We present algorithms to determine if a graph has a k-

doi:10.21711/231766362021/rmc485
fatcat:7edkr5mayzah5bnv3jrmvwbmfa
*biclique*-coloring: an O * (4 n )-time algorithm using exact*cover*,*and*an O * (k + 2) 2dtime FPT algorithm, where d is*the*neighborhood diversity*of*... A k-*biclique*-coloring*of*G is k-coloring*of**the*vertices*of*G with no maximal monochromatic*biclique*. A recent work showed that determining if such a coloring exists is Σ P 2 -complete for k > 2. ... Since B ∪ {u} is a*biclique*, Proj(u) is adjacent to only*one**partition**of*B ′ . ...##
###
Exact exponential-time algorithms for finding bicliques

2010
*
Information Processing Letters
*

Due to a large number

doi:10.1016/j.ipl.2010.10.020
fatcat:auug2gskdfelrpykz5mrvyswwm
*of*applications,*bicliques**of*graphs have been widely considered in*the*literature. This paper focuses*on*non-induced*bicliques*. ...*The*NP-complete problem*of*finding a non-induced (k 1 , k 2 )-*biclique*asks to decide whether G contains a non-induced*biclique*(X, Y ) such that |X| = k 1*and*|Y | = k 2 . ... We already mentioned that CBVC,*the**parameterized*dual*of*Non-induced (k 1 , k 2 )*Biclique*, is in FPT. It is a natural question to ask whether Non-induced (k 1 , k 2 )*Biclique*is in FPT as well. ...##
###
Efficient Approximation for Restricted Biclique Cover Problems

2018
*
Algorithms
*

*The*decision version

*of*

*the*minimum

*biclique*

*cover*problem is NP-Complete,

*and*unless P = NP,

*the*

*cover*size cannot be approximated in general within less than a sub-linear factor

*of*

*the*number

*of*nodes ... We show that this practical version

*of*

*the*

*biclique*

*cover*problem is amenable to efficient approximations. ...

*The*research was partially supported by NSF grant IIS-1247581

*and*NIH grant R01-CA180776. Conflicts

*of*Interest:

*The*authors declare no conflicts

*of*interest. ...

##
###
A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms
[article]

2020
*
arXiv
*
pre-print

*Parameterization*

*and*approximation are two popular ways

*of*coping with NP-hard problems. More recently,

*the*two have also been combined to derive many interesting results. ... We survey developments in

*the*area both from

*the*algorithmic

*and*hardness perspectives, with emphasis

*on*new techniques

*and*potential future research directions. ... Conflicts

*of*Interest:

*The*authors declare no conflict

*of*interest. ...

##
###
Preprocessing Subgraph and Minor Problems: When Does a Small Vertex Cover Help?
[article]

2013
*
arXiv
*
pre-print

We prove a number

arXiv:1206.4912v3
fatcat:yady3pi7krfwjajng3z3ni4x3u
*of*results around kernelization*of*problems*parameterized*by*the*size*of*a given vertex*cover**of**the*input graph. ... While our characterization captures many interesting problems,*the*kernelization*complexity*landscape*of**parameterizations*by vertex*cover*is much more involved. ... In*parameterized*graph algorithms,*one**of**the*most important*and*relevant*complexity*measures*of*a graph is its treewidth. ...##
###
A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

2020
*
Algorithms
*

*Parameterization*

*and*approximation are two popular ways

*of*coping with NP-hard problems. More recently,

*the*two have also been combined to derive many interesting results. ... We survey developments in

*the*area both from

*the*algorithmic

*and*hardness perspectives, with emphasis

*on*new techniques

*and*potential future research directions. ... Conflicts

*of*Interest:

*The*authors declare no conflict

*of*interest. ...

##
###
Graph Square Roots of Small Distance from Degree One Graphs
[article]

2020
*
arXiv
*
pre-print

We are interested in

arXiv:2010.05733v1
fatcat:43jifxqrfjcyvjplbcvdejbl4e
*the**parameterized**complexity**of**the*problem for classes ℋ that are composed by*the*graphs at vertex deletion distance at most k from graphs*of*maximum degree at most*one*, that is, ... We show that different variants*of**the*problems with constraints*on**the*number*of*isolated vertices*and*edges in H-S are FPT when*parameterized*by k by demonstrating algorithms with running time 2^2^O( ... Note that if B has a*biclique**cover**of*size strictly less than k, we can add arbitrary*bicliques*to this*cover**and*obtain a*biclique**cover*for B*of*size exactly k. ...##
###
Characterizing the easy-to-find subgraphs from the viewpoint of polynomial-time algorithms, kernels, and Turing kernels
[chapter]

2014
*
Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms
*

if G contains t vertexdisjoint subgraphs isomorphic to H. do not give a complete characterization

doi:10.1137/1.9781611973730.42
dblp:conf/soda/JansenM15
fatcat:k67ttnsabjcitiaox6khfgcfpe
*of**the*cases when F-Subgraph Test admits polynomial many-*one*kernels, but show examples that this question ... We study two fundamental problems related to finding subgraphs: (1) given graphs G*and*H, Subgraph Test asks if H is isomorphic to a subgraph*of*G, (2) given graphs G, H,*and*an integer t, Packing asks ... for*the*many-*one**complexity**of*F-Subgraph Test. ...##
###
Computing Dense and Sparse Subgraphs of Weakly Closed Graphs
[article]

2020
*
arXiv
*
pre-print

Comp. 2020]

arXiv:2007.05630v2
fatcat:woyutwltbzfeflz6yd5j7z4njm
*on*clique enumeration, we show that several problems related to finding dense subgraphs, such as*the*enumeration*of**bicliques**and*s-plexes, are fixed-parameter tractable with respect to γ(G ... This graph parameter is never larger than*the*degeneracy (plus*one*)*and*can be significantly smaller. Extending*the*work*of*Fox et al. [SIAM J. ... For more details*on**parameterized**complexity*, we refer to*the*standard monographs [5, 7] . Variants*of*Independent Set In this section we study Independent Set*and*related problems. ...##
###
On the Fine-Grained Complexity of Rainbow Coloring

2018
*
SIAM Journal on Discrete Mathematics
*

We show that

doi:10.1137/16m1102690
fatcat:27emtdloibf3vbpf4ny75mxc4i
*the*problem is FPT when*parameterized*by q*and*has a kernel*of*size O(q) for every k ≥ 2, extending*the*result*of*Ananth et al. [FSTTCS 2011]. ... We believe that our techniques used for*the*lower bounds may shed some light*on**the**complexity**of**the*classical Edge Coloring problem, where it is a major open question if a 2 O(n) -time algorithm exists ... Then*the*edges ofḠ can be*covered*by O(p 2 ∆ 1 (G) log n)*bicliques*fromḠ so that any edge*of*G*and*any*biclique*have at most*one*common vertex. ...##
###
A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems
[article]

2022
*
arXiv
*
pre-print

We survey both older

arXiv:2204.10526v1
fatcat:ua3pkqxtabatbbl6jydhy3i3b4
*and*more recent work*on**the**parameterized**complexity**of*all three problems when*parameterized*by*the*number*of*tokens k. ...*The*emphasis will be*on*positive results*and**the*most common techniques for*the*design*of*fixed-parameter tractable algorithms. ... We survey both older*and*more recent work*on**the**parameterized**complexity**of*all three problems when*parameterized*by*the*number*of*tokens k. ...
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